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You probably just forgot to write the word operator after the word vector.
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
https://en.wikipedia.org/wiki/Divergence
From the point of view of physics (and in a strict sense and in the sense of intuitive physical image of a mathematical operation) the divergence of a vector field is a measure of the extent to which a given point of space (or rather a sufficiently small neighborhood of a point) is a source or a drain of this field:
div F>0 — point field is the source;
div F<0 — the field point is a drain;
div F=0-there are no drains and sources, or they compensate for each other
It is quote from the Russian-language version of Wikipedia, the English-language version does not have this
https://ru.wikipedia.org/wiki/Дивергенция

Let's write Newton's law of universal gravitation in the differential form
div g = - G*ro
The divergence Operator shows where the field has a drain and where it has a source. If the divergence is positive at a given point in space, it means that the source of the field is there, and if it is negative, then the flow of the field is there.From the above equation, it follows that the gravitational field has only drains. Where are the origins? in infinity? But then gravity must propagate at an infinite speed, which is not true. So where is the origin of the gravitational field?

The electromagnetic field with its mass and momentum creates gravity, which changes the direction of movement of electromagnetic waves.
In this case, gravity is an additional source of gravity or anti-gravity. I'm leaning toward the latter.

NASA researchers conducted experiments in Antarctica and found evidence that a parallel universe, like our own, was formed as a result of the Big Bang.
https://www.forbes.com/sites/jamiecartereurope/2020/05/21/has-nasa-found-a-parallel-universe-where-time-flows-backwards-the-truth-behind-the-headlines/#211c18e0646d
NASA researchers discovered high-energy neutrinos in Antarctica that were moving away from the center of the earth into space. This should not happen because high energy neutrinos that came from space from the other side of the earth should be absorbed in the earth's core. But since they were discovered, it was concluded that they came from a parallel universe and time for these particles goes in the direction opposite to the flow of our time.
And if you look for another explanation for this, a more mundane one. For example, it has been repeatedly reported that the glaciers of Antarctica are melting under the action of geothermal heat from a tectonic fault.
http://www.plateclimatology.com/west-antarctic-ice-sheet-melting-from-geothermal-heat-not-global-warming
We can assume that under Antarctica, close to the surface of the earth, there are nuclear reactions that are the source of these high-energy neutrinos, and then the eruption of a supervolcano should be expected more likely in Antarctica, and not in Sumatra or Yellowstone national Park

I believe that in accordance with the third law of Hegel's dialectics ( development goes in a spiral), physics will somehow return to the ether as a medium for the propagation of interactions. Of course, not to the Lorentz model, but on a new level. Most likely, the term "ether" itself will be replaced with another one.However, this is already happening, because the vacuum in the modern sense is not a void.

Saoussen Mbarek and Manu Paranjape at the Université de Montréal in Canada say they’ve found a solution to Einstein’s theory of general relativity that allows negative mass without breaking any essential assumptions. Their approach means that negative mass can exist in our universe provided there is a reasonable mechanism for producing it, perhaps in pairs of positive and negative mass particles in the early universe.
https://medium.com/the-physics-arxiv-blog/cosmologists-prove-negative-mass-can-exist-in-our-universe-250a980320a7

According to Hawking, the energy of space is negative. Excerpt from Stephen Hawking's final book
"To help you understand this strange but important idea, let me draw a simple analogy. Imagine a person who wants to make a hill on an even place. The hill is the universe. To implement his plan, our man needs to dig a hole in the ground and use the soil to fill the hill. In other words, it creates not only a hill, but also a pit, which is essentially a negative version of the hill. The substance that was in the pit is now in the hill, so everything is perfectly balanced. The same principle underlies the creation of the Universe.
When the Big Bang produced a huge amount of positive energy, it simultaneously produced the same amount of negative energy. Thus, negative and positive energy add up to zero-as usual. Another law of nature.
Where is all this negative energy now? In the third ingredient of our cosmic cooking recipe — in space. It may seem strange, but according to the laws of nature related to gravity and dynamics — one of the oldest scientific laws — space is a huge store of negative energy. Enough to balance everything and reduce it to zero."

If we consider the gravitational field as a medium for the propagation of electromagnetic waves, the refractive index of this medium can be described by a very simple formula
N=sqrt (Phi)/c
this formula shows that the refractive index N depends only on the gravitational potential of Phi and does not depend on the frequency of photons, that is, there will be no dispersion in this medium.
Photons propagate in a physical vacuum, and even if there are 0 protons per cubic kilometer in it, still from the point of view of modern physics, a vacuum is not a torricellian void, that is, a vacuum can be considered as a material medium.
Yes, OP's mode cannot be considered a full-fledged theory of gravity, but it can be considered a theory of the interaction of gravity and electromagnetism.